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Clocking the Deck
Clocking the deck is one of the oldest recorded card amusements. One of Leonardo da Vinci's contemporaries, Luca Pacioli, included the idea in his Perugia manuscript “Tractatus mathematicus ad discipulos Perusinos” (Vat. Lat. 3129), 1477-1478, f. 226r, as Problem 21: “Also, if someone were to take one card out of the entire deck, [here is] how to find it in two steps.”
The idea showed up in English in Thomas Johnson's Dainty Conceits, 1630, p. 10. In French, it was Problem XXXII in Chapter I of Jacques Ozanam's Récréations mathématiques et physiques, 1694. (See here for an English translation from 1708.) And Reinhard Müller has found the system in German in Natürliches Zauberbuch, 1745, p. 230. These all rely on the idea of canceling tens in the counting.
Friedrich Wilhelm Conradi gives an elaboration of the feat in his book Magisches Allerlei, 1903, p.102. He adds up the value and the suit at the same time, in two columns of numbers. He then expands the effect, letting a spectator call out any number and the performer names the card at that number.