In fact, no relationship of the Maya linguistic group to any other has been discovered. It contains a number of words borrowed from the Aztec (Nahuatl); and the latter in turn presents many undoubtedly borrowed from the Maya dialects. But this only goes to show that these two great families had long and close relations; and that we already know, from their history, traditions and geographical positions. § 6. _The Numeral System._ The Mayas had a mathematical turn, and possessed a developed system of numeration. It counted by units and scores; in other words, it was a vigesimal system. The cardinal numbers were:-- Hun, one. Ca, two. Ox, three. Can, four. Ho, five. Uac, six. Uuc, seven. Uaxac, eight. Bolon, nine. Lahun, ten. Buluc, eleven. Lahca, twelve. Oxlahun, thirteen. Canlahun, fourteen. Holhun, fifteen. Uaclahun, sixteen. Uuclahun, seventeen. Uaxaclahun, eighteen. Bolonlahun, nineteen. Hunkal, twenty. The composition of these numerals from twelve to nineteen inclusive is easily seen. _Lahun_ is apparently a compound of _lah hun_ (sc. _uinic_), "it finishes one (man);" that is, in counting on the fingers. _Lah_ means the end, to end, and also the whole of anything. _Kal_, a score, is literally a fastening together, a shutting up, from the verb _kal_, to shut, to lock, to button up, etc. From twenty upward, the scores are used:-- Hun tu kal, one to the score, 21. Ca tu kal, two to the score, 22. Ox tu kal, three to the score, 23, and so on up to Ca kal, two score, 40. Above forty, three different methods can be used to continue the numeration. 1. We may continue the same employed between 20 and 40, thus:-- Hun tu cakal, one to two score, 41. Ca tu cakal, two to two score, 42. Ox tu cakal, three to two score, 43, and so on. 2. The numeral copulative _catac_ can be used, with the numeral particle _tul_; as:-- Cakal catac catul, two score and two, 42. Cakal catac oxtul, two score and three, 43. 3. We may count upon the next score above, as: Hun tu yoxkal, one on the third score, 41. Ca tu yoxkal, two on the third score, 42. Ox tu yoxkal, three on the third score, 43. The last mentioned system is that advanced by Father Beltran, and is the only one formally mentioned by him. It has recently been carefully analyzed by Prof. Leon de Rosny, who has shown that it is a consistent vigesimal method.[40-1]