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Boole's Published Works

Reproduced with the kind permission of Desmond MacHale, author of The Life and Work of George Boole: Prelude to the Digital Age (Cork University Press, 2014)

Key Books

1847

The Mathematical Analysis of Logic, being an Essay towards a Calculus of Deductive Reasoning
Macmillan, Barclay and Macmillan, Cambridge.

1854

An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities
Walton and Maberley, London.

1859

A Treatise on Differential Equations
Macmillan, Cambridge.

1860

A Treatise on the Calculus of Finite Differences
Macmillan, Cambridge.

Key Papers

1841

Researches on the Theory of Analytical Transformations, with a special application to the Reduction of the General Equation of the Second Order
Cambridge Mathematical Journal, vol. 2, pp. 64–73.

1842

Exposition of a General Theory of Linear Transformations. Part I
Cambridge Mathematical Journal, vol. 3, pp. 1–20.

Exposition of a General Theory of Linear Transformations. Part II
Cambridge Mathematical Journal, vol. 3, pp. 106–119.

1844

On a General Method in Analysis
Philosophical Transactions of the Royal Society, vol. 134, pp. 225–282.

1845

Notes on Linear Transformations
Cambridge Mathematical Journal, vol. 4, pp. 167–171.

On the Equation of Laplace’s Functions
Report of the British Association for the Advancement of Science, Cambridge, Part 2, p. 2.

1847

On the Attraction of a Solid of Revolution on an External Point
Cambridge and Dublin Mathematical Journal, vol. 2, pp. 1–7.

1848

Notes on Quaternions
Philosophical Magazine, vol. 33, no. 3, pp. 278–280.

Theorème général concernant l’intégration definie
Liouville’s Journal de Mathématique, vol. 13, pp. 111–112.

1851

An Account of the late John Walsh of Cork In a letter from Professor Boole to Professor de Morgan
Philosophical Magazine, vol. 2, no. 4, pp. 348–358.

1855

The Social Aspects of Intellectual Culture
An Address to the Cuvierian Society, Cork.

1857

On the Application of the Theory of Probabilities to the Question of the Combination of Testimonies or Judgements
Transactions of the Royal Society of Edinburgh, vol. 21, pp. 597–653.

1863

Über die partielle Differentialgleichung zweiter Ornung Rr+Ss+Tt+U (s2-rt) = V
Crelle’s Journal der Mathematik, vol. 61, pp. 309–333.


1865, translated into English with additional remarks, as Chapter XXIX in A Treatise on Differential Equations: Supplementary Volume edited by Isaac Todhunter. Macmillan, Cambridge.

Bibliography Continued

Ode to the Spring (1830) The Lincoln Herald, dated May 28th.

Letter to the Editor (1830) The Lincoln Herald, dated June 12th.

Letter to the Editor (1830) The Lincoln Herald, dated June 26th.

Lines to a Departed Friend, From the Greek (1830) The Lincoln Herald, dated July 15th.

To the Evening Star, From the Greek of Bion (1830) The Lincoln Herald, dated August 25th.

An Address on the Genius and Discoveries of Sir Isaac Newton (1835) Gazette Office, Lincoln.

Researches on the Theory of Analytical Transformations, with a special application to the
Reduction of the General Equation of the Second Order (1841) Cambridge
Mathematical Journal, Vol. 2, pp. 64-73.

On Certain Theorems in the Calculus of Variations (1841) Cambridge Mathematical
Journal, Vol. 2, pp. 97-102.

On the Integration of Linear Differential Equations. with Constant Coefficients (1841)
Cambridge Mathematical Journal, Vol. 2, pp. 114-119.

Analytical Geometry (1841) Cambridge Mathematical Journal, Vol. 2, pp. 179-188.

Exposition of a General Theory of Linear Transformations. Part I (1842) Cambridge
Mathematical Journal, Vol. 3, pp. 1-20.

Exposition of a General Theory of Linear Transformations. Part II (1842) Cambridge
Mathematical Journal, Vol. 3, pp. 106-119.

On the Transformation of Definite Integrals (1843) Cambridge Mathematical Journal, Vol.
3, pp. 216-224.

Remarks on a Theorem of M. Catalan (1843) Cambridge Mathematical Journal, Vol. 3, pp.
277-283.

On a General Method in Analysis (1844) Philosophical Transactions of the Royal Society,
Vol. 134, pp. 225-282.

On the Transformation of Multiple Integrals (1845) Cambridge Mathematical Journal,
Vol. 4, pp. 20-28.

On the Inverse Calculus of Definite Integrals (1845) Cambridge Mathematical Journal,
Vol. 4, pp. 82-87.

Notes on Linear Transformations (1845) Cambridge Mathematical Journal, Vol.4, pp.
167-171.

On the Theory of Developments. Part I (1845) Cambridge Mathematical Journal, Vol. 4,
pp. 214-223.

On the Equation of Laplace's Functions (1845) Report of the British Association for the
Advancement of Science, Cambridge, Part 2, p. 2.

On the Equation of Laplace's Functions (1846) Cambridge and Dublin Mathematical
Journal, Vol. 1, pp. 10-22.

The Mathematical Analysis of Logic, being an Essay towards a Calculus of Deductive
Reasoning (1847) Macmillan, Barclay and Macmillan, Cambridge.

The Right Use of Leisure (1847) London.

On a Method of Definite Integration (1847) Report of the British Association for the
Advancement of Science, Oxford, Part 2, p. 2.

On the Attraction of a Solid of Revolution on an External Point (1847) Cambridge and
Dublin Mathematical Journal, Vol. 2, pp. 1-7.

On a certain Symbolical Equation (1847) Cambridge and Dublin Mathematical Journal
Vol. 2, pp. 7-12.

Remarks on the Rev. B. Bronwin's Method for Differential Equations (1847) Philosophical
Magazine, Vol. 30, No. 3, pp. 6-8.

Note on a Class of Differential Equations (1847) Philosophical Magazine, Vol. 30, No. 3,
pp. 96-97.

A Memoir on Discontinuous Functions (1848) Proceedings of the Royal Irish Academy, Vol.
3, pp. 182-184.

On a certain Definite Multiple Integral (1848) Proceedings of the Royal Irish Academy, Vol.
3, pp. 217-218. .

Remarks on a Paper by the Rev. Brice Bronwin, On the Solution of a particular Differential
Equation (1848) Philosophical Magazine, Vol. 32, No.-3, pp. 413-418.

Letter to the Editor concerning Remarks on a Paper by the Rev. Brice Bronwin, On the Solution of a particular Differential Equation (1848) Philosophical Magazine, Vol. 33, No. 3, p. 211.

Notes on Quaternions (1848) Philosophical Magazine, Vol. 33, No. 3, pp. 278-280.

Theoreme general concernant l'integration definie (1848) Liouville's Journal de
Mathematique, Vol. 13, pp. 111-112.

On the Analysis of Discontinuous Functions (1848) Transactions of the Royal Irish
Academy, Vol. 21, pp. 124-139.

On a certain Multiple Definite Integral (1848) Transactions of the Royal Irish Academy,
Vol. 21, pp. 140-149.

On a General Transformation of any Quantitative Function (1848) Cambridge and Dublin
Mathematical Journal, Vol. 3, pp. 112-116.

The Calculus of Logic (1848) Cambridge and Dublin Mathematical Journal, Vol. 3, pp. 183-198.

Mr. Boole's Theory of the Mathematical Basis of Logic (1848) Mechanics' Magazine,
Vol. 49, pp. 254-255.

Supplementary Investigations on Discontinuous Functions and Definite Multiple
Integrals (1848) Proceedings of the Royal Irish Academy, Vol. 3, pp. 292-294.

On a General Theorem of Definite Integration (1849) Cambridge and Dublin Mathematical
Journal, Vol. 4, pp. 14-20.

The Claims of Science, especially as founded in its Relations to Human Nature (1851) London.

On the Theory of Linear Transformations (1851) Cambridge and Dublin Mathematical
Journal, Vol. 6, pp. 87-106.

On the Reduction of the General Equation of the nth Degree. (Sequel to a Memoir on the Theory of Linear Transformations)(1851) Cambridge and Dublin Mathematical Journal, Vol. 6, pp. 106-113.

Letter to the Editor (1851) Cambridge and Dublin Mathematical Journal, Vol. 6, pp. 284-285.

Proposed Question in the Theory of Probabilities (1851) Cambridge and Dublin
Mathematical Journal, Vol. 6, p. 286.

On the Theory of Probabilities and in particular on Mitchell's Problem of the Distribution
of the Fixed Stars (1851) Philosophical Magazine, Vol. 1, No. 4, pp. 521-530.

Further Observations on the Theory of Probabilities (1851) Philosophical Magazine, Vol.
2, No. 4, pp. 96-101.

An Account of the late John Walsh of Cork (1851) In a letter from Professor Boole to
Professor de Morgan. Philosophical Magazine, Vol. 2, No. 4, pp. 348-358.

On Reciprocal Methods in the Differential Calculus (1852) Cambridge and Dublin
Mathematical Journal, Vol. 7, pp. 156-166.

On Reciprocal Methods in the Differential Calculus, continued (1853) Cambridge and
Dublin Mathematical Journal, Vol. 8, pp. 1-24.

An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of
Logic and Probabilities (1854) Walton and Maberley, London.

Solution of a Question in the Theory of Probabilities (1854) Philosophical Magazine, Vol.
7, No. 4, pp. 29-32.

Reply to some Observations published by Mr. Wilbraham in the Philosophical Magazine,
Vol. vii, p. 465, on the Theory of Chances developed in Professor Boole's Laws of
Thought (1854) Philosophical Magazine, Vol. 8, No. 4, pp. 87-91.

On the Conditions by which the Solutions of Questions in the Theory of Probabilities are
limited (1854) Philosophical Magazine, Vol. 8, No. 4, pp. 91-98.

Further Observations relating to the Theory of Probabilities in reply to Mr. Wilbraham
(1854) Philosophical Magazine, Vol. 8, No. 4, pp. 175-176.

On a General Method in the Theory of Probabilities (1854) Philosophical Magazine, Vol. 8,
No. 4, pp. 431-444.

The Social Aspects of Intellectual Culture (1855) An Address to the Cuvierian Society.
Cuvierian Society, Cork.

On certain Propositions in Algebra connected with the Theory of Probabilities (1855)
Philosophical Magazine, Vol. 9, No. 4, pp. 165-179.

On the Solution of the Equation of Continuity of an Incompressible Fluid (1856) Letter
to Rev. Charles Graves, May 5th, 1856. Proceedings of the Royal Irish Academy, Vol. 6,
pp. 375-386.

Letter to the Editor (1856) Cork Daily Reporter, November 13th.

Letter to the Editor (1856) Cork Daily Reporter, November 27th.

On the Comparison of Transcendents, with certain applications to the Theory of Definite
Integrals (1857) Philosophical Transactions of the Royal Society, Vol. 147, pp. 745-804.

On the Theory of Astronomical Observations, and on some Related Questions (1857)
Report of the British Association for the Advancement of Science, Dublin, Part 2, p. 2.

On certain Additions to the Integral Calculus (1857) Report of the British Association for the
Advancement of Science, Dublin, Part 2, p. 2.

On the Application of the Theory of Probabilities to the Question of the Combination of
Testimonies or Judgements (1857) Transactions of the Royal Society of Edinburgh, Vol.
21, pp. 597-653.

Evidence to the Queen's Colleges Commission (1858) Report of Her Majesty's
Commissioners appointed to inquire into the Progress and Condition of the Queen's Colleges,
H.M. Government, Dublin, pp. 171-174, 201-203.

Curriculum for the Degree of BA and MA in the Queen's University (1858) Report of Her
Majesty's Commissioners, H.M. Government, Dublin, pp. 327-328.

Letter to Dr. Ryall (1859) An Investigation into the condition of the children in the Cork
Workhouse, by John Arnott, MP (privately published pamphlet). Cork.

A Treatise on Differential Equations (1859) Macmillan, Cambridge.

A Treatise on the Calculus of Finite Differences (1860) Macmillan, Cambridge.

On the Theory of Probabilities (1862) Philosophical Transactions of the Royal Society, Vol.
152, pp. 225-252.

On Simultaneous Differential Equations of the first order in which the number of variables
exceeds by more than one the number of the equations (1862) Philosophical
Transactions of the Royal Society, Vol. 152, pp. 437-454.

On Simultaneous Differential Equations in which the Number of Variables exceeds by more than unity the Number of Equations (1862) Proceedings of the Royal Society, Vol. 12, p. 184.

On the Differential Equations of Dynamics (1862) Report of the British Association for the
Advancement of Science, Cambridge, Part 2, p. 3.

Some Observations by Professor Boole (contained in On a Question in the Theory of
Probabilities, by A. Cayley) (1862) Philosophical Magazine, Vol. 23, No. 4, pp.
361-365.

Supplement to a paper On the Differential Equations of Dynamics (1862) Proceedings of
the Royal Society, Vol. 12, p. 481.

Considerations sur la recherche des integraies premieres des equations differentielles
partielles du second ordre (1862) Bulletin de l'Academie Imperiale des Sciences de St.
Petersbourg, Vol. 4, pp. 198-215.

On the Differential Equations of Dynamics. A Sequel to a paper On Simultaneous
Differential Equations (1863) Philosophical Transactions of the Royal Society, Vol. 153,
pp. 485-501.

Ueber die partielle Differentialgleichung zweiter Ornung Rr+Ss+Tt+U (S2 -rt) = V (1863)
Crelle's Journal der Mathematik, Vol. 61, pp. 309-333. (Translated into English, with additional remarks, as Chapter XXIX in A Treatise on Differential Equations: Supplementary Volume (1865) Edited by Isaac Todhunter. Macmillan, Cambridge.)

On the Theory of Probabilities (1863) Philosophical Magazine, Vol. 25, No. 4, pp. 313-317.

On the Differential Equations which determine the form of the Roots of Algebraic
Equations (1864) Proceedings of the Royal Society, Vol. 13, pp. 245-246.

On the Differential Equations which determine the form of the Roots of an Algebraic
Equation (1864) Philosophical Transactions of the Royal Society, Vol. 154, pp. 733-755.

A Treatise on Differential Equations: Supplementary Volume (1865) Edited by Isaac
Todhunter. Macmillan, Cambridge.

Of Propositions numerically Definite (1871) Published posthumously, written about 1850. Transactions of the Cambridge Philosophical Society, Vol. 11, pp. 396-411.

Boole's Collected Logical Works, Volume II (1916) Edited by P.E.B. Jourdain. Open Court, Chicago and London. (Volume I, which was meant to contain a full-length biography of Boole, never appeared.)

Mary Everest Boole: Collected Works (1931) Edited by E.M. Cob ham, 4 Volumes, C.W.
Daniel, Essex. These volumes contain poems by George Boole: The Fellowship of the
Dead; Three Aspects of Nature; Ten Years Later; To the Number Three; The Lord sitteth
above the Water-Flood and the Lord remaineth a King forever; The Communion of Saints;
Ode to Truth; The Council of Constance.

Studies in Logic and Probability by George Boole (1952) Edited by Rush Rhees. Watts and
Co., London. This contains: Sketch of a Theory and Method of Probabilities founded upon the Calculus of Logic. Written between 1848 and 1854. Pp.141-166; Logic and Reasoning. Title postulated by Rush Rhees (Editor). pp. 211-229; On the Mathematical Theory of Logic and on the Philosophical Interpretation of its Methods and Processes (extracts).
Written in 1855 or 1856. pp. 230-246. These three papers are based on previously
unpublished manuscripts by Boole, held in the Library of the Royal Society, London.

The Boole - De Morgan Correspondence, 1842-1864 (1982) Edited by G.C. Smith.
Clarendon Press, Oxford.