The seventeenth century saw the birth of the true mechanical calculator—several times over. First came Schickard's "calculating clock" (built 1623), which could add, subtract, multiply, and divide. Knowledge of Schickard's device was lost upon his death, however, and not recovered until the twentieth century. After Schickard's clock came Pascal's calculating machine or "Pascaline" (built 1642), which, though it saw extensive actual use, could only add and subtract.

Pascal never saw Schickard's device, and Gottfried Wilhelm von Leibniz, the German philosopher and law professor who built the world's next mechanical calculator, never saw either Schickard's or Pascal's. Leibniz's "Step Reckoner," as he called it (built 1674), could do all that its predecessors had done and could do it better, for Leibniz devised an improved solution to the most vexing problem of mechanical calculation: the carry operation. In performing addition, for example, when one digit changes from...