## On a General Method in Analysis (Boole, pp. 225-282) WITH Observations on some of the nebulae (Parsons, pp. 321-324) In Philosophical Transactions of the Royal Society of London 134, 1844

London: The Royal Society, 1844. 1st Edition. FULL VOLUME BOUND FIRST EDITION WITH BOOLE’S IMPORTANT CONTRIBUTION TO THE THEORY OF LINEAR DIFFERENTIAL EQUATIONS & ROSSE’S OBSERVATIONS OF ‘CRAB NEBULA’ AS WELL AS HIS WELL KNOWN RENDERING.

GEORGE BOOLE: “The English mathematician and philosopher George Boole (1815-1864) was one of the first men (after Leibniz) who believed that the human thinking is mastered by laws, which can be described by means of mathematic. Boole is the inventor of Boolean logic, which is the basis of modern digital computer logic, thus Boole is regarded in hindsight as a founder of the field of computer science” (History-Computer Portal).

Boole received the Royal Society’s Gold Medal for the work offered here, the first ever awarded for mathematics. The paper is a lengthy work “on differential equations, combining an exponential substitution and variation of parameters with the separation of symbols method” (Stanford Encyclopedia of Philosophy). Sometimes described as Boole’s “first mathematical masterpiece [this paper] is a work grounded on the laws of combination of non-commutative symbols, which apparently convinced Boole of the immense power afforded by symbolical methods, a power largely due to their main property of not depending upon conditions of their interpretation” ” (Panteki, The Mathematical Background, Boole Anthology, 167).

Boole’s efforts were a significant contribution to the theory of linear differential equations, moving from the case of constant coefficients to variable coefficients. “The paper investigates differentiation and differential equations from an operator point of view and introduces Boole’s new ‘algebra of classes’” (George Boole 200 Portal). This ‘Boolean algebra’ contributed to freeing mathematics from number systems, and pushed mathematics a step further towards abstraction. Boole’s innovation in operational methods are in use today.

Boole’s “general method in analysis, originally described in his famous memoir printed in the Philosophical Transactions for 1844 [offered here]. Boole was one of the most eminent of those who perceived that the symbols of operation could be separated from those of quantity and treated as distinct objects of calculation. His principal characteristic was perfect confidence in any result obtained by the treatment of symbols in accordance with their primary laws and conditions, and an almost unrivalled skill and power in tracing out these results” (NNDB).

EARL OF ROSSE: In 1844 and using a 36 inch telescope, William Parsons, 3rd Earl of Rosse observed an object that came to be referred to as the ‘Crab Nebula’ largely based on the details of Rosse’s drawings (included in this volume). Now understood to be a supernova remnant, the nebula was named because its tentacle-like structure, so clearly evidenced in the drawings, resembled the legs of the crustacean. Also now understood is that the bright designs of the Crab Nebula come from a filamentary structure of hot gasses combined with a mass of electrons trapped within the leftover pulsar's powerful magnetic field.

ALSO: Gassiot, A Description of an Extensive Series of the Water Battery, pp. 39-51. Gassiot had found that “the static effects of effects of tension produced by a voltaic battery were in some direct ratio with the chemical energies of the substances of which the battery was composed” (Gassiot, 1844). His “work was particularly important in the demise of the contact theory of voltaic electricity” (WP).

ALSO: Fownes, On the Existence of Phosphoric Acid in Rocks of Igneous Origin, pp. 53-56. Fownes discovered the presence of phosphate in igneous rocks and suggested that this was the original source of phosphate in clay and soil. Item #1246

CONDITION: Complete volume. 4to. Bearing only a single stamp on the title page and a blind stamp. 28 plates. Handsomely rebound in calf; 5 raised spine bands; red & black morocco spine labels. Original wide margins; minor toning to a few plates, otherwise bright and clean within. Near fine.

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Price:
$625.00
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