Heron also wrote _Pneumatica_ (where the reader will find such things as siphons, Heron's Fountain, penny-in-the-slot machines, a fire-engine, a water-organ, and many arrangements employing the force of steam), _Automaton-making_, _Belopoeïca_ (on engines of war), _Catoptrica_, and _Mechanics_. The _Mechanics_ has been edited from the Arabic; it is (except for considerable fragments) lost in Greek. It deals with the puzzle of 'Aristotle's Wheel', the parallelogram of velocities, definitions of, and problems on, the centre of gravity, the distribution of weights between several supports, the five mechanical powers, mechanics in daily life (queries and answers). Pappus covers much the same ground in Book VIII of his _Collection_. We come, lastly, to Algebra. Problems involving simple equations are found in the Papyrus Rhind, in the _Epanthema_ of Thymaridas already referred to, and in the arithmetical epigrams in the Greek Anthology (Plato alludes to this class of problem in the _Laws_, 819 B, C); the Anthology even includes two cases of indeterminate equations of the first degree. The Pythagoreans gave general solutions in rational numbers of the equations _x²+y²=z²_ and _2x²-y²=±1_, which are indeterminate equations of the second degree. The first to make systematic use of symbols in algebraical work was Diophantus of Alexandria (fl. about A. D. 250). He used (1) a sign for the unknown quantity, which he calls αριθμος {arithmos}, and compendia for its powers up to the sixth; (2) a sign ([Transcriber's Note: Symbol]) with the effect of our _minus_. The latter sign probably represents ΛΙ {LI}, an abbreviation for the root of the word λειπειν {leipein} (to be wanting); the sign for αριθμος {arithmos} ([Transcriber's Note: Symbol]) is most likely an abbreviation for the letters αρ {ar}; the compendia for the powers of the unknown are Δ^Υ {D^Y} for δυναμις {dynamis}, the square, Κ^Υ {K^Y} for κυβος {kybos}, the cube, and so on. Diophantus shows that he solved quadratic equations by rule, like Heron. His _Arithmetica_, of which six books only (out of thirteen) survive, contains a certain number of problems leading to simple equations, but is mostly devoted to indeterminate or semi-determinate analysis, mainly of the second degree. The collection is extraordinarily varied, and the devices resorted to are highly ingenious. The problems solved are such as the following (fractional as well as integral solutions being admitted): 'Given a number, to find three others such that the sum of the three, or of any pair of them, together with the given number is a square', 'To find four numbers such that the square of the sum _plus_ or _minus_ any one of the numbers is a square', 'To find three numbers such that the product of any two _plus_ or _minus_ the sum of the three is a square'. Diophantus assumes as known certain theorems about numbers which are the sums of two and three squares respectively, and other propositions in the Theory of Numbers.