Miscellaneous Investigations between
1750 and 1780
-  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.
-  Kaestner recieved the prize for his work on the subject of
fortuitous events proposed by the Académie Royale. It is his
Dissertation sur les devoirs qui resultent de la conviction, que les
èvenemens fortuits dependent de la volonté de dieu. Todhunter remarks
that it is useless.
-  E.C. Canz.
Tractatio synoptica de probabilitate juridica sive de praesumtione.
-  Corbyn Morris. Observations
on the past growth and present state of the City of London. To which
are annexed a complete table of the Christnings and Burials within this
City from 1601 to 1750... together with a table of the numbers which
have annually died of each disease from 1675 to the present time. London.
-  Nicholas Struyck. Vervolg van de Beschryving
der Staartsterren, en nader Ontdekkingen omtrent den Staat van't Menschelyk
Geslagt, etc. 2 parts. Amsterdam. Volume I and
-  Edmond Hoyle (1672-1769). An essay towards making the doctrine of chances easy to those
who understand vulgar arithemtick only. London: J. Jolliff. New corrected edition (1764). Hoyle, of course, is the Hoyle of the famous Rules of Games.
- [1754-5] Pehr Wargentin. "Om nyttan af Forteckningar pa födda och döda i et Land." (Swedish) Kongl. Vetenskaps Acad., 16, pp. 81-96.
- [1754-68] Anton Friedrich Büsching. Neue Erdebeschreibung. Hamburg. English translation of Pts 1-4 by P. Murdoch (1762). A New System of Geography: in which is given, a general account of ... the several kingdoms and states in the known world... 6 vols. Volume I, Vol 2, Vol 3, Vol 4, Vol 5 and Vol 6. London: A. Miller.
-  C. Maire & R.C. Boscovich. De litteraria
expeditione per Pontificiam ditionem ad dimetiendos duos Meridiani gradus et
corrigendam mappam geographicam, jussu et auspiciis Bnedicti XIV, Pont.
Max., ... Romae. French translation by Hugon (1770).
-  A work by Jacopo Belgrado entitled
Dell'azione del caso nelle invenzioni, e dell' influsso degli astri ne'corpi terrestri, dissertazioni due. Padova. Todhunter remarks that this is
-  G. Burrington. An answer to Dr. William
Brakenridge's letter concerning the number of inhabitants, within the London
Bills of Mortality. Wherein the doctor's letter is inserted... his arguments
proved inconclusive, and the number of inhabitants increasing. London:
-  V. de Forbonnais. Recherches et
considérations sur les Finances de France depuis 1595 jusqu'à 1721.
Tome 1 and
Tome 2, and
-  Samuel Clark
Laws of Chance: or, a mathematical investigation of the probabilities
arising from any proposed circumstances of play. Applied to the
solution of a great variety of problems relating to cards, bowls, dice,
lotteries, etc. London: T. Payne. This work is based upon those of Moivre and Simpson.
It contains nothing of importance.
-  James Postlethwayt. IV. A comparative view of the diseases and ages,
and a table of the probabilities of life for the last thirty years. A
collection of the yearly Bills of Mortality from 1657 to 1758,
inclusive. Together with several other Bills of an earlier date. 2 pt. London.
-  R.G. Boscovich. De recentissimis graduum dimensionibus, et figura, ac magnitudine terrae inde derivanda. Philosophiae recentioris ... versibus tradititae libri x (By Benedictus Stay), 2, 406-26.
- [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.
-  Alexis Fontaine. Here we
have a posthumous work dealing with the Petersburg problem.
-  G. von Vega. Thesaurus logarithmorum completus. The
link is to the English edition (1906). Note the criticism.
-  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
-  Johann Andreas Groschius. Logica probabilium in artium practicarum subsidum adornata. Halae.
-  Friedrich Wilhelm Morpurg. Die Kunst sein Glück spielend zu mache. Hamburg.
- [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.
-  Mesaance. Recherches
sur la population des Généraliités de'Auvergne, de Lyon, de Rouen, et
de quelques provinces et villes du royaume avec des réflexions sur la
valeur du bled tant en France qu'en Angleterre depuis 1674 jusqu'en 1764. Paris.
-  J.L. Muret. Mèmoire sur l'état de la population dans le pays de Vaud. Yverdon.
-  C. Garve. De nonnulis quae pertinent ad logicam probabilium. Halae.
-  Pehr Wargentin. Mortaliteten i sverige, i anledning af tabell-verket.
Kongl. Vetenskaps Acad. 27. English translation (1930); Mortality in
Sweden according to the "Tablell-Verket" (General Register Office).
-  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
-  Richard Price. Observations
on the expectations of lives, the increase of mankind, the influence of
great towns on population, and particularly the state of London, with
respect to healthfulness and number of inhabitants... In a letter ...
to Benjamin Franklin. London: W. Bowyer and J. Nichols.
-  Hugon.
Voyage astronomique et géographique dans l'Etat de Église ... pour mésurer
deux degrés du Méridien, et corriger la Carte de l'Etat Ecclésiastique...
-  Johann Lambert. We have
a paper on superstition.
-  Arthur Young. Proposals to the legislature
for numbering the people.
-  Richard Price. Observations
on reversionary payments;... To which are added four essays on
different subjects in the doctrine of life annuities and political
arithmetic. Also, an appendix, containing...tables, shewing the
probabilities of life in London, Norwich, and Northampton; and the
values of joint lives. London: T. Cadell. 2nd ed. (1772); 3rd ed. (1773); 4th ed. (1783) 2 vols: Volume I and Volume II.; 5th ed. (1792) 2 vols. to which are added, algebraical notes... by W. Morgan; 6th ed. (1803) 2 vols.
-  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.
-  J. Fenn. Calculations and formulae for
determining the advantages or disadvantages of gamesters.
-  J. Fenn First Letter to the Dublin Society of the use of Mathematical Reasoning in Civil, Moral, and Political Enquiries. Dublin. The proposed series of letters echoes Chapter IV of the Ars Conjectandi of Jakob Bernoulli This first letter by Fenn concerns the game of tennis. Bernoulli himself addressed this game in a separate work: Letter à un
amy sur les parties du jeu de paume.
-  H. Proctor. The Sportsman's Sure Guide, or the Gamesters's Vademecum showing the exact Odds at Horse Racing, Lotteries, etc.
-  C.H. Frömmichen.
Über die Lehre des Wahrscheinlichen. Braunschweig.
Jean Dusaulx. Lettre et Réflexions sur la fureur du jeu. This is a meditation on games. See pages 3 - 64.
-  Samuel Clark. Considerations
upon lottery schemes in general; containing a minute investigation of
the real and eventual profits arising to lottery offices... Together
with a full examination of Mr. Molesworth's celebrated schemes for
pointing out... fortunately inclined numbers. London: Printed for the author.
-  M. Lastri. Ricerche
sull'antica e moderna poplazione della Città de Firenze, per mezzo dei
registri ael battistero di S. Giovanni dal 1451 al 1774. Firenze.
-  E. Wigglesworth. Calculations on American population: with a table for estimating the annual increase of inhabitants in the British Colonies.
-  William Emerson. Probability. Miscellanies, or, a miscellaneous treatise, containing several mathematical subjects. (London).
-  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.
-  Moheau.
Recherches et considérations sur la population de la France. 2 tom.
-  Jean Dusaulx. De la passion du jeu. This examines games from ancient times to the present.
-  E. Waring. Problems concerning interpolation.
- [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.