Summa de Arithmetica
Luca Pacioli, 1494
Lequal cose le hanno assai piu legiermente ale mani: se ancora le mani de la Arithmetica haueremo amente: lequal seruiran sempre a tutte ditte parti: si conmo dinanze promise mostrare.
These things are much more easily done with the hands—provided that we keep in mind the “hands” of arithmetic, which will always serve for all the said parts, just as I promised to show before.
E pongotele parti figurate che sonno 18 sinistre. E altre tante dextre che in tutto fra ambedoi formano 36 acti per ognuna 18.
And I set before you the positions (figures), which are eighteen on the left hand and as many on the right; together they make thirty-six gestures, eighteen for each hand.
E i la sinistra si compone sin cento unita e fornito el centinaro se loca in la mã dextra. e cosi li migliara: peroche si fa in quella.
The left hand is used to compose the units up to one hundred; and once a hundred is completed, it is placed on the right hand. The same is done for the thousands, because they are formed there.
Per centina e migliara conmo in la sinistra: si fa de numeri e dicine. Per numeri inteso quasi menore de 10 conmo altre volte hai inteso.
For hundreds and thousands, just as on the left hand one forms numbers and tens, so on the right hand one does the same. By “numbers” I mean those less than ten, as you have understood before.
Thus, the first gesture of the first left hand signifies 1; the second gesture signifies 2; the third signifies 3; the fourth, 4; the fifth, 5; the sixth, 6; the seventh, 7; the eighth, 8; the ninth, 9; the tenth, 10; the eleventh, 20; the twelfth, 30; the thirteenth, 40; the fourteenth, 50; the fifteenth, 60; the sixteenth, 70; the seventeenth, 80; the eighteenth, 90.
Unde el pº acto de la p'ª mã sinistra dici. 1. El. 2ª. de la. 2ª. dici. 2. El 3ª. de la. 3ª dici 3. E la 4ª.4. E la 5ª. 5. E la. 6ª. 6. E la. 7ª. 7. E la. 8ª. 8. E la. 9ª. 9. E la. xª. 10. E la. 11. 20. E la. 12ª. 30. E la. 13ª. 40. E la. 14ª. 50. E la. 15ª. 60. E la. 16ª. 70. E la. 17ª. 80. E la. 18ª. 90.
E cosi farai per li centinara e migliara a la man dextra facendo li medesimi acti per un centinaro e per un migliaro etc. e andarai ponendo ale mani sin dieci milia: cioe tanto numero. 10000. che piu oltra mal te seruano etc.
And you will do likewise for the hundreds and thousands on the right hand, making the same gestures for a hundred and for a thousand, and so on. In this way, you will go on counting on the hands up to ten thousand — that is, to the number 10,000 — beyond which they are of little further use.
Source: Luca Pacioli, Summa de arithmetica, geometria, proportioni et proportionalita (Venice: Paganinus de Paganinis, 1494), fol. 36r.