“OUR DEBT TO THIS SIMPLE, QUIET MAN, GEOGE BOOLE, IS EXTRAORDINARILY GREAT” (ORIGINS OF CYBERSPACE):RARE FIRST EDITION OF THE 1841 CAMBRIDGE MATHEMATICAL JOURNAL (II), THE FIRST PUBLICATION OF FOUR MAJOR PAPERS BY GEORGE BOOLE

BOOLE, George. Researches on the Theory of Analytical Tranformations, With a Special Application to the Reduction of the General Equation of the Second Order. BOUND WITH: Analytical Geometry (i.e. Symmetrical Solutions of Problems Respecting the Straight Line and Plane). BOUND WITH: On Certain Theorems in the Calculus of Variations. BOUND WITH: On the Integration of Linear Differential Equations with Constant Coefficients. IN: The Cambridge Mathematical Journal. Vol. II. Cambridge, England: E. Johnson, 1841. Octavo, original brown cloth, original printed paper spine label, uncut and partially unopened. Housed in a custom clamshell box.

First edition of scarce and important 1841 Cambridge Mathematical Journal, Volume II, containing the first publication of four major early papers by British mathematician George Boole, whose life work and the invention of the first practical system logic in algebraic form—Boolean algebras— “enabled more advances in logic to be made in the decades of the 19th century than in the 22 centuries preceding” (Origins of Cyberspace 224).

This complete Volume II of the Cambridge Mathematical Journal, containing six issues that run from November 1839 to May 1841, offers the first publication of over 20 major papers in the fields of plane geometry, calculus, algebra, analytical geometry, astronomy and mechanics. Of chief importance in this rare volume is the first publication of four major papers by prominent 19th-century British mathematician George Boole, whose life work ultimately “led to the creation of set theory and probability theory in mathematics, to the philosophical work of Peirce, Russell, Whithead and Wittengenstein, and to computer technology… ‘Since Boole showed that logics can be reduced to very simple algebraic systems— known today as Boolean Algebras— it was possible for Babbage and his successors to design organs for a computer that could perform the necessary logical tasks. Thus our debt to this simple, quiet man, George Boole, is extraordinarily great” (Origins of Cyberspace 224). Largely self-educated, in 1840 Boole first began to contribute papers this Journal, as well the Royal Society, “which awarded him a Royal Medal in 1844 for his papers on operators in analysis; he was elected a fellow of the Royal Society in 1857.”

This important volume contains Boole’s “Researches on the Theory of Analytical Transformations, With a Special Application to the Reduction of the General Equation of the Second Order” (64-73); “On Certain Theorems in the Calculus of Variations” (97-102); “On the Integration of Linear Differential Equations with Constant Coefficients” (114-119) and “Analytical Geometry” (179-188). In these four major papers and those published in the Journal in 1843, “Boole dealt with linear transformations. He showed that if the linear transformation x = pX + qY, y = rX + sY is applied to the binary quadratic form ax² + 2hxy + by² to yield the binary quadratic form AX² + 2HXY + BY², then AB H² = (ps qr)² (ab h²). The algebraic fact had been partly perceived by Lagrange and by Gauss, but Boole’s argument drew attention to the (relative) invariance of the disciminant ab h ², and also to the absolute invariants of the transformation. This was the starting point of the theory of invariants… Boole greatly increased the power of the operational calculus… His two-valued algebra has recently been applied to the design of electric circuits containing simple switches, relays and control elements. In particular, it has a wide field of application in the design of high speed computers using the binary system of digital numeration” (DSB II:294-8). These important early papers signal the vital contributions and influence of this revolutionary mathematician whose invention of the first practical system of logic in algebraic form “enabled more advances in logic to be made in the decades of the 19th century than in the 22 centuries preceding” (Origins of Cyberspace 224). This Volume II of the Cambridge Mathematical Journal contains: November 1839 (No. VII), February 1840 (No. VIII), May 1840 (No. IX), November 1840 (No. X), February 1841 (No. XI) and May 1841 (No. XII). With four folding plates. Bookseller ticket.

Text generally fresh and clean, slight edge-wear, some soiling to original cloth. A highly desirable extremely good copy of this seminal scientific work.