Miscellaneous Investigations between
1750 and 1780
- 1748 James Dodson: The Mathematical Repository. This work
is dedicated to Abraham DeMoivre. Volume
I concerns algebra problems. Volume
II,containing probability problems on pages 82-136, appeared in
1753; The remainder of Volume II and Volume III (1755) are
dedicated to annuities. The second
edition was published in 1775.
- 1754 Edmond Hoyle (1672-1769): An
Essay towards making the Doctrine of Chances Easy to those who
Understand Vulgar Arithmetic Only. This link points to a
revised edition of 1764. Hoyle, of course, is the Hoyle of the famous Rules of Games.
- 1758 Samuel Clark The
Laws of Chance. This work is based upon those of Moivre and Simpson.
It contains nothing of importance.
- 1762 & 1772 Jacques-Andre
Mallet. Mallet contributed a paper on Waldegrave's problem which
was first treated in Montmort's Jeux de Hazard, Problem 14 of the Ars Coniectandi of Jakob Bernoulli and the Lottery
of Lorraine also treated in Montmort.
- 1764 Alexis Fontaine. Here we
have a posthumous work dealing with the Petersburg problem.
- 1767 John Michell. "An
Inquiry into the probable Parallax, and Magnitude of the fixed Stars,
from the Quantity of Light which they afford us, and the particular
Circumstances of their Situation," by the Rev. John Michell, B.D.
F.R.S. This paper was read on May 7 and 14, 1767 and published in the Philosophical Transactions
.
- 1849-1850 James David Forbes: Forbes critiques Michell in two
articles "On the alleged Evidence for a Physical Connexion between
Stars forming Binary or Multiple Groups, arising from their Proximity
alone," published in the London,
Edinburgh and Dublin Philosophical Magazine, August
1849 (pp. 132-133) & December
1850 (pp.401-427).
- 1765-1769 Jean Bernoulli III.
He has contributed a paper on the duration of marriages, a problem on
which Daniel Bernoulli wrote, and
a paper on the Genoise Lottery.
- 1765 & 1768 Nicolaus
Béguelin. Nicolaus wrote a Memoir in two parts on the
Genoise Lottery in which he unifies the work of Euler and Jean Bernoulli III and another
memoir related to d'Alembert's concerns of the foundations of
probability and also on the Petersburg problem.
- 1768 Richard Price. Four
Dissertations. The fourth part is entitled: On the Importance of Christianity, the
Nature of Historical Evidence, and Miracles. Although not
properly mathematical, it is related due to its discussion of testimony
and miracles.
- 1771 Johann Lambert. We have
a paper on superstition.
- 1771 Moses Mendelssohn. (1729-1786) Publication of his Philosophical Writings, Volume
I and Volume
II. See pages 241-283 of the second volume for "Über die
Wahrschienlichkeit." In Philosophical
Writings, an English translation has been made by Daniel
Dahlstrom (1997) Cambridge pp. 233-250.
- 1775 Jean Dusaulx. Lettre et Réflexions sur la fureur du jeu. This is a meditation on games. See pages 3 - 64.
- 1776 William Emerson: Miscellanies
or a miscellaneous treatise.
- 1777 Georges-Louis Leclerc, Comte
de Buffon: The supplement to his Natural
History contains the Essai
D'Arithmétique Morale which treats the Petersburg Problem
and Geometric Probability including the Buffon Needle Problem. For the
Petersburg Problem see both Niklaus
Bernoulli and Daniel Bernoulli.
- 1779 Jean Dusaulx. De la passion du jeu. This examines games from ancient times to the present.
- 1779-1780 Nicolas Fuss. In two
papers, Fuss deals also with Problem 14 proposed by Jakob Bernoulli in the Ars Coniectandi. He learned of the
problem by reading Mallet.