Energyequations, such as the above, may be operated with precisely as if they were algebraic equations, a property which is of great advantage in calculation.
Often assumptions are made which lead to equations in x which cannot be solved "rationally," i.e.
The distribution of weight in chemical change is readily expressed in the form of equations by the aid of these symbols; the equation 2HC1+Zn =ZnCl2+H2, for example, is to be read as meaning that from 73 parts of hydrochloric acid and 65 parts of zinc, 136 parts of zinc chloride and 2 parts of hydrogen are produced.
Jahn, 2 the processes at the anode can be represented by the equations 2CH 3 000+H 2 0 =2CH3 000H+0 2 C H 3.
Among the great variety of problems solved are problems leading to determinate equations of the first degree in one, two, three or four variables, to determinate quadratic equations, and to indeterminate equations of the first degree in one or more variables, which are, however, transformed into determinate equations by arbitrarily assuming a value for one of the required numbers, Diophantus being always satisfied with a rational, even if fractional, result and not requiring a solution in integers.