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## Boole's Published Works

### Key Books

**1847**

**1854**

**1859**

**1860**

### Key Papers

**1841**

**1842**

**1844**

**1845**

**1847**

**1848**

**1851**

**1855**

**1857**

**1863**

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)

*The Mathematical Analysis of Logic, being an Essay towards a Calculus of Deductive Reasoning*

Macmillan, Barclay and Macmillan, Cambridge.

*An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities*

Walton and Maberley, London.

*A Treatise on Differential Equations*

Macmillan, Cambridge.

*A Treatise on the Calculus of Finite Differences*

Macmillan, Cambridge.

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.

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.

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

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.

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

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.

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.

*The Social Aspects of Intellectual Culture*

An Address to the Cuvierian Society, Cork.

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.

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.