Besides the hieroglyphical maps, the traditions of the country were embodied in the songs and hymns, which, as already mentioned, were carefully taught in the public schools. These were various, embracing the mythic legends of a heroic age, the warlike achievements of their own, or the softer tales of love and pleasure.[172] Many of them were composed by scholars and persons of rank, and are cited as affording the most authentic record of events.[173] The Mexican dialect was rich and expressive, though inferior to the Tezcucan, the most polished of the idioms of Anahuac. None of the Aztec compositions have survived, but we can form some estimate of the general state of poetic culture from the odes which have come down to us from the royal house of Tezcuco.[174] Sahagun has furnished us with translations of their more elaborate prose, consisting of prayers and public discourses, which give a favorable idea of their eloquence, and show that they paid much attention to rhetorical effect. They are said to have had, also, something like theatrical exhibitions, of a pantomimic sort, in which the faces of the performers were covered with masks, and the figures of birds or animals were frequently represented; an imitation to which they may have been led by the familiar delineation of such objects in their hieroglyphics.[175] In all this we see the dawning of a literary culture, surpassed, however, by their attainments in the severer walks of mathematical science. They devised a system of notation in their arithmetic sufficiently simple. The first twenty numbers were expressed by a corresponding number of dots. The first five had specific names; after which they were represented by combining the fifth with one of the four preceding; as five and one for six, five and two for seven, and so on. Ten and fifteen had each a separate name, which was also combined with the first four, to express a higher quantity. These four, therefore, were the radical characters of their oral arithmetic, in the same manner as they were of the written with the ancient Romans; a more simple arrangement, probably, than any existing among Europeans.[176] Twenty was expressed by a separate hieroglyphic,--a flag. Larger sums were reckoned by twenties, and, in writing, by repeating the number of flags. The square of twenty, four hundred, had a separate sign, that of a plume, and so had the cube of twenty, or eight thousand, which was denoted by a purse, or sack. This was the whole arithmetical apparatus of the Mexicans, by the combination of which they were enabled to indicate any quantity. For greater expedition, they used to denote fractions of the larger sums by drawing only a part of the object. Thus, half or three-fourths of a plume, or of a purse, represented that proportion of their respective sums, and so on.[177] With all this, the machinery will appear very awkward to us, who perform our operations with so much ease by means of the Arabic or, rather, Indian ciphers.