The Maya had three concurrent counts: 365-day years; 360-day `years' (tuns), with named vigesimal multiples to 3200000 tuns, for calculations; and a 260-day sacred almanac (13 numbers and 20 concurrent names) covering all mundane and astronomical activities. Solar eclipse and Venus synodical revolutions are tabulated in one hieroglyphic book to reach the lowest common multiple with 260: for Venus 37960 days (584 × 65 = 260 × 146 also 365 × 104); for the Moon 11960 days (405 lunations = 260 × 46). The Maya successfully predicted eclipses, but were unaware of which would be visible to them. Means were astronomical; ends, astrological. Ingenious corrections, also retaining the 260-day connexion, occur. The corrected error in Venus revolutions is one day in 6000 years. Lunar corrections similarly had to conform to the sacred almanac. Other planetary tables are very dubiously identified. Solar data are challengeable. Dates are recorded 5 million, possibly 90 and 400 million years ago.