b. 4 November 1744 Basel, Switzerland
d. 13 July 1807 Berlin, Germany
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Johann III, son of Johann II and grandson of Johann
I, at the invitation
of Frederick II, went to the Berlin Academy to reorganize the
observatory
in 1764. Between 1766 and 1775 he published in the Histoire de
l'Academie
des sciences et belles lettres de Berlin in which may be found two
papers
concerning probability. In general, his papers are of little interest.
"Mémoire sur
un probleme de la Doctrine du Hazard," Histoire de l'Academie
des sciences et belles lettres de Berlin for 1768, (1770), pp.
384-408.
This paper concerns the following problem: Any number of persons of
one same age, half men, half women, are married together the same year,
to find the probability that, the half of this complete number of
married persons being dead, all the marriages will be broken.
This paper is only slightly related to that of Daniel
Bernoulli "De
duratione
matrimoniorum media pro quacunque coniugum aetate, aliisque
quaestionibus affinibus." Novi Commentarii Acad. Petrop.
Vol. XII, 1766/7 (1768), pp. 99-126. See also the paper by Jean Trembley: "Observations sur les calculs relatifs
à la durée des mariages et au nombre des époux
subsistans." Mémoires de l'Académie des
sciences et belles-lettres...Berlin, 1799/1800, pp. 110-130. It was
published in 1803.
"Sur les suites ou
séquences dans la loterie de Genes," Histoire de
l'Academie des sciences et belles lettres de Berlin for 1769, Vol.
25 (1771), pp. 234–253.
On the Genoese lottery, see the several papers of Leonard Euler where are linked a large
number of other related works. In this lottery there are 90 tickets
numbered consecutively from among which 2, 3,4 or 5 are drawn at
random. Jean Bernoulli seeks the probability distribution of sequences
formed by these extracted tickets. The numbers are assumed to be
arranged as in a circle so that 90-1 forms a sequence of length 2,
89-90-1 a sequence of length 3 and so forth. Nicolaus Béguelin unites the
work of Euler and Bernoulli in a paper published in the Acta Helvetica
in 1765.
Besides these, to him is attributed the entry Milieu in the Encyclopédie Methodique. Its three volumes devoted to mathematics were published in 1784, 1785 and 1789 respectively. The article summarizes the work of others. These include Josef Boskovich, Johann Heinrich Lambert, Daniel Bernoulli and Joseph Lagrange. The paper of Daniel Bernoulli was later published as Dijudicatio maxime probabilis plurium observationum discrepantium; atque verisimillima inductio inde formanda. The account given does not correspond to that published in Acta Acad. Petrop. for 1777, pars prior with date of publication 1778. The memoir of Lagrange is Mémoire sur l'utilité de la méthode de prendre le milieu entre les résultats de plusieurs observations; dan lequel on examine les avantages de cette méthode par le calcul des probabilités; et où l'on résoud différens problêmes relatifs à cette matière, published in Miscellanea Taurinensia Vol. V for 1770-1773, pp. 167 - 232 of the mathematical portion.
Birkhäuser Verlag plans an edition of Johann III Bernoulli, Werke.