# Ternary Sentence Examples

- Bibliographical references to
**ternary**forms are given by Forsyth (Amer. - This view was accepted in 1817 by Leopold Gmelin, who, in his Handbuch der Chemie, regarded inorganic compounds as being of binary composition (the simplest being oxides, both acid and basic, which by combination form salts also of binary form), and organic compounds as
**ternary**, i.e. - The idea_can be generalized so as to have regard to
**ternary**and higher forms each of the same order and of the same number of variables. **Ternary**and Higher Forms.-The**ternary**form of order n is represented symbolically by (aixl+a2x2+a3x3)' =a'; and, as usual, b, c, d,...**Ternary**and Higher Forms.-The**ternary**form of order n is represented symbolically by (aixl+a2x2+a3x3)' =a'; and, as usual, b, c, d,...- For example, take the
**ternary**quadratic (aixl+a2x2+a3x3) 2 =a2x, or in real form axi +bx2+cx3+2fx 2 x 3+ 2gx 3 x 1 +2hx i x 2. - The
**ternary**cubic has been investigated by Cayley, Aronhold, Hermite, Brioschi and Gordan. - Hesse showed independently that the general
**ternary**cubic can be reduced, by linear transformation, to the form x3+y3+z3+ 6mxyz, a form which involves 9 independent constants, as should be the case; it must, however, be remarked that the counting of constants is not a sure guide to the existence of a conjectured canonical form. - Thus the
**ternary**quartic is not, in general, expressible as a sum of five 4th powers as the counting of constants might have led one to expect, a theorem due to Sylvester. - This is of degree 8 in the coefficients, and degree 6 in the variables, and, for the canonical form, has the expression -9m 6 (x 3 +y 3 +z 3) 2 - (2m +5m 4 +20m 7) (x3 +y3+z3)xyz - (15m 2 +78m 5 -12m 8) Passing on to the
**ternary**quartic we find that the number of ground forms is apparently very great. - The system of two
**ternary**quadratics consists of 20 forms; it has been investigated by Gordan (Clebsch-Lindemann's Vorlesungen i. - Ciamberlini has found a system of 127 forms appertaining to three
**ternary**quadratics (Batt. - For the unipartite
**ternary**quantic of order n he finds that the fundamental system contains a (n+4) (n -1) individuals. - Of the Memoir he discusses bi-
**ternary**quantics, and in particular those which are lineo-linear, quadrato-linear, cubo-linear, quadrato-quadratic, cubo-cubic, and the system of two lineo-linear quantics. - For instance, those of a
**ternary**form involve two classes which may be geometrically interpreted as point and line co-ordinates in a plane; those of a quaternary form involve three classes which may be geometrically interpreted as point, line and plane coordinates in space. - The alloy of the point e is the
**ternary**eutectic; it deposits the three metals simultaneously during the whole period of its solidfication and solidifies at a constant temperature. - It is evident that any other property can be represented by similar diagrams. For example, we can construct the curve of conductivity of alloys of two metals or the surface of conductivity of
**ternary**alloys, and so on for any measurable property. - This subject is far from being exhausted, and it is not improbable that the alloy-producing capacity of aluminium may eventually prove its most valuable characteristic. In the meantime,
**ternary**light alloys appear the most satisfactory, and tungsten and copper, or tungsten and nickel, seem to be the best substances to add. - The British method is a mixture of the last two, but with an index-scale which is partly
**ternary**and partly binary. - We have in the Hessian the first instance of a covariant of a
**ternary**form. - The theory of the invariants and covariants of a
**ternary**cubic function u has been studied in detail, and brought into connexion with the cubic curve u = o; but the theory of the invariants and covariants for the next succeeding case, the**ternary**quartic function, is still very incomplete. - If a compound contains two atoms it is termed a binary compound, if three a
**ternary**, if four a quaternary, and so on. - He successfully considers the systems of two and three simultaneous
**ternary**quadratics. - He shows that the system of the bi-
**ternary**n°m i ° comprises 4 (n+1)(n+2)(m+1)(m+2)- 3 individuals. - The
**ternary**alloys containing bismuth, tin and lead have been studied in this way by F.