## Nouvelle Arithmetique binaire (pp. 71-76) WITH Explication de l'Arithmetique Binaire (pp. 105-111) in Histoire et Memoires de l’Academie Royale des Sciences Annee 1707 [FIRST AMSTERDAM EDITION OF BOTH OF LEIBNIZ'S SEMINAL WORKS ON BINARY ARITHMETIC]

Amsterdam: Chez Gerard Kuyper. FIRST AMSTERDAM EDITION OF TWO SEMINAL WORKS ON BINARY ARITHMETIC BY GOTTFRIED LEIBNIZ. Together, these two papers describe Leibniz’s development of a binary system – a decisive prerequisite for digital technology and the foundation of virtually all modern computer architectures.

“Leibniz was the first mathematician thoroughly to study the binary system upon which all modern digital computers are based”; he was also one of the first people to appreciate base-two binary arithmetic and the fact that everything can be represented using only ones and zeroes" (Heilbron, J.L., ed, The Oxford Companion to the History of Modern Science, p. 172; Chaitin, Gregory. “Leibniz, Randomness & the Halting Probability).

The volume offered here is the Amsterdam edition of Leibniz’s fundamental treatises on the binary system, Nouvelle Arithmetique binaire and Explication de l'Arithmétique Binaire. The papers are here collected in a single volume whereas when first published in France in 1705, the papers appeared in separate volumes.

Though he didn’t publish his ideas for many years, in 1679, Leibniz conceived the application of binary arithmetic to computing, imagining a “a digital computer in which binary numbers were represented as spherical pellets, circulating within a kind of pinball machine governed by a rudimentary form of punched-card control.

‘This [binary] calculus could be implemented by a machine (without wheels),’ he wrote, ‘in the following manner, easily to be sure and without effort. A container shall be provided with holes in such away that they can be opened and closed. They are to be open at those places that correspond to a 1 and remain closed at those that correspond to a 0. Through the opened gates small cubes or marbles are to fall into tracks, through the other nothing. It [the gate array] is to be shifted from column to column as required.’ In the shift of registers at the heart of the electronic microprocessor voltage gradients and pulses of electrons have taken the place of gravity and marbles, but otherwise things are running exactly as envisioned by Leibniz in 1679” (Dyson, George. Darwin Among the Machines: The Evolution of Global Intelligence, p. 37).

Though the machine Leibniz conceived was never built , the two papers included here laid the foundation for Boolean algebra and digital circuitry which was continued by George Boole, Augustus De Morgan, and Claude Shannon in the centuries following.

ALSO INCLUDED: Other important works by Cassini, de la Hire, Tournefort, and Varignon are included. Item #1566

CONDITION & DETAILS: Complete. Amsterdam: Chez Gerard Kuyper. 16mo. [6], 12, [6 table of contents], 571, [7]. NOT an ex-library book; small ownership signature on title page. Bound in contemporary vellum, stamped in gold leaf on the front and rear boards. The binding is solid, tight, and very clean though the hand-lettered spine is somewhat sun darkened. The text-block is nicely red edged. Woodcut vignette on the title page and engraved historiated frontispiece; woodcut head- and tailpieces. 11 engraved plates as well as woodcut illustrations and diagrams throughout. Bright and exceptionally clean throughout.

Price: \$8,000.00